11 citations · 45 across the 26 of their papers we have counts for
22 papers · 1 filter
Rigidity of the Julia set for Hénon-Sibony maps
Gabriel Vigny
Let and be two Hénon-Sibony maps of . We show that if they have the same forward Julia set, then they share a common iterate, thereby extending Lamy's results…
Quantitative equidistribution of periodic points for rational maps
Thomas Gauthier, Gabriel Vigny
We show that periodic points of period of a complex rational map of degree equidistribute towards the equilibrium measure of the rational map with a rate of convergen…
Julia sets and bifurcation loci
Thomas Gauthier, Gabriel Vigny
We prove that several dynamically defined fractals in and which arise from different type of polynomial dynamical systems can not be the same objects. O…
Exponential mixing of all orders and CLT for generic birational maps of
Henry De Thélin, Gabriel Vigny
For Hénon maps, Bianchi and Dinh recently proved the exponential mixing of all orders for the measure of maximal entropy and, as a consequence of the recent work of Björklund and G…
The Geometric Dynamical Northcott Property in the quadratic family
Thomas Gauthier, Gabriel Vigny
The aim of this note is to give a proof of Theorem A from our work on the geometric Northcott property in the simpler case of the quadratic family; being in dimension in both t…
Sparsity of postcritically finite maps of and beyond: A complex analytic approach
Thomas Gauthier, Johan Taflin, Gabriel Vigny
An endomorphism of degree is said to be postcritically finite (or PCF) if its critical set is preperiodic, i.e. if there…